The orbit of Comet 1941c-1941IV /De Kock-Paraskevopoulos/
Calculating orbit for Comet 1941c -1941IV using least squares method, and considering planetary perturbations
Van Biesbroeck, G.↗
SEARCH · Search NASA
Results for “LEAST SQUARES METHOD”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On the determination of near body orbits using mass concentration models
Mathematical model for near-body orbit calculation using mass concentration, perturbation theory, nonlinear equations, geopotentials, and least squares method
Childs, B.↗
San Marco satellite attitude determination based on aerodynamic drag measurements
San Marco satellite attitude determination from onboard aerodynamic drag measurements, using least squares method for three components calculation
Hunziker, R. R.↗
Atomic emission line wavelength calculations below 2000 angstroms for Lithium II through Cobalt XXVI
Atomic-emission-line wavelengths are presented which were calculated from wavelengths of previously identified transition sequences using second-degree polynomials fitted to known wave numbers by the least squares method. Wavelengths less than 2000 angstroms are included for ions from Li II to Co XXVI. The computer program written in FORTRAN 4 is also included.
Williams, M. D.↗
Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations
Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.
Miller, C. D.↗
Neutron die-away experiment for remote analysis of the surface of the moon and the planets, phase 3
Continuing work on the two die-away measurements proposed to be made in the combined pulsed neutron experiment (CPNE) for analysis of lunar and planetary surfaces is described. This report documents research done during Phase 3. A general exposition of data analysis by the least-squares method and the related problem of the prediction of variance is given. A data analysis procedure for epithermal die-away data has been formulated. In order to facilitate the analysis, the number of independent material variables has been reduced to two: the hydrogen density and an effective oxygen density, the latter being determined uniquely from the nonhydrogeneous elemental composition. Justification for this reduction in the number of variables is based on a set of 27 new theoretical calculations. Work is described related to experimental calibration of the epithermal die-away measurement. An interim data analysis technique based solely on theoretical calculations seems to be adequate and will be used for future CPNE field tests.
Mills, W. R.↗
Polynomial approximations of thermodynamic properties of arbitrary gas mixtures over wide pressure and density ranges
Computer programs for flow fields around planetary entry vehicles require real-gas equilibrium thermodynamic properties in a simple form which can be evaluated quickly. To fill this need, polynomial approximations were found for thermodynamic properties of air and model planetary atmospheres. A coefficient-averaging technique was used for curve fitting in lieu of the usual least-squares method. The polynomials consist of terms up to the ninth degree in each of two variables (essentially pressure and density) including all cross terms. Four of these polynomials can be joined to cover, for example, a range of about 1000 to 11000 K and 0.00001 to 1 atmosphere (1 atm = 1.0133 x 100,000 N/m sq) for a given thermodynamic property. Relative errors of less than 1 percent are found over most of the applicable range.
Allison, D. O.↗
ERTS orbit maintenance
Error drift in the ERTS orbit maintenance problem is determined from the actual ground trace errors that the spacecraft experienced over the first 3 1/2 repeat cycles. Actual data are fitted to a parametric model of ground trace error by a least squares method, and initial offsets to these key parameters as well as their rates of change are extrapolated forward analytically to obtain the future ground trace drift in orbital estimates.
Fuchs, A. J.↗
Slosh testing of a spherical mercury propellant tank with positive-expulsion diaphragm
A preliminary investigation was conducted to evaluate the lateral slosh characteristics of a 23-cm diameter mercury propellant tank with a positive-expulsion diaphragm and 17.5% ullage. Data are presented for tank sinusoidal acceleration levels between 0.05 and 0.5 g at frequencies ranging from 5 to 50 Hz. Results indicate that slosh characteristics are highly nonlinear at acceleration levels approaching those in flight, and depend heavily on the shape and stiffness of the diaphragm. Nyquist plots of driving force over acceleration are shown to be a useful tool for determining natural frequency, damping, and modal mass characteristics. A computerized nonlinear least squares method for extracting the modal parameters from the Nyquist plots is described and results of applying the method are presented.
Ross, R. G., Jr.↗
Analysis of longitudinal thickness-shear stiffness of a monolayer filamentary composite
The longitudinal thickness-shear behavior of a rectangular cross-section prism containing circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Saint-Venant flexure problem modeled by a tip-loaded cantilever composite beam and solution is obtained by the boundary-point least-squares method. It is shown that the longitudinal thickness-shear modulus is much greater than the in-plane shear modulus for a monofilament composite and therefore an independent analysis is necessary to predict the longitudinal thickness-shear behavior of the composite. Numerical results are presented in graphical form for various values of fiber volume fraction and material parameters typical of modern advanced composites.
Chang, S.↗
X-ray structural study of chrome-aluminum lunar spinel from the Sea of Fertility
An X-ray structural study was made of a lunar spinel sample from the Sea of Fertility. The chemical composition and distribution of cations in the structure were characterized. Interpretation of the experimental data by the least squares method yielded the oxygen parameter u = 0.261 and the isotropic temperature factor 1.09 AU squared.
Nozik, Y. Z.↗
Analysis of twisting stiffness for a multifiber composite layer
The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.
Bert, C. W.↗
In situ ply strength: An initial assessment
The in situ ply strengths in several composites were calculated using laminate fracture data for appropriate low modulus, and high modulus fiber composites were used in conjunction with the least squares method. The laminate fracture data were obtained from tests on Modmor-I graphite/epoxy, AS-graphite/epoxy, boron/epoxy and E-glass/epoxy. The results show that the calculated in situ ply strengths can be considerably different from those measured in unidirectional composites, especially the transverse strengths and those in angleplied laminates with transply cracks.
Chamis, C. C.↗
Stress analysis for structures with surface cracks
Two basic forms of analysis, one treating stresses around arbitrarily loaded circular cracks, the other treating stresses due to loads arbitrarily distributed on the surface of a half space, are united by a boundary-point least squares method to obtain analyses for stresses from surface cracks in places or bars. Calculations were for enough cases to show how effects from the crack vary with the depth-to-length ratio, the fractional penetration ratio, the obliquity of the load, and to some extent the fractional span ratio. The results include plots showing stress intensity factors, stress component distributions near the crack, and crack opening displacement patterns. Favorable comparisons are shown with two kinds of independent experiments, but the main method for confirming the results is by wide checking of overall satisfaction of boundary conditions, so that external confirmation is not essential. Principles involved in designing analyses which promote dependability of the results are proposed and illustrated.
Bell, J. C.↗
Error in total ozone measurements arising from aerosol attenuation
A generalized least squares method for deducing both total ozone and aerosol extinction spectrum parameters from Dobson spectrophotometer measurements was developed. An error analysis applied to this system indicates that there is little advantage to additional measurements once a sufficient number of line pairs have been employed to solve for the selected detail in the attenuation model. It is shown that when there is a predominance of small particles (less than about 0.35 microns in diameter) the total ozone from the standard AD system is too high by about one percent. When larger particles are present the derived total ozone may be an overestimate or an underestimate but serious errors occur only for narrow polydispersions.
Thomas, R. W. L.↗
Velocity structure of the shallow lunar crust
Data from the thumper shots of the Apollo 14 and Apollo 16 active seismic experiments, testing whether the velocity variation in the shallow lunar crust (depths less than or equal to 10 m) can be represented by a self-compacting-power-layer or by a constant-velocity-layer model, are analyzed. Although filtering and stacking improved the S/N ratios, it was found that measuring the arrival times or amplitudes of arrivals beyond 32 m was not possible. The data quality precluded a definitive distinction between the power-law velocity variation and the layered-velocity model. Furthermore, it was found that the shallow lunar regolith is made up of fine particles, which supports the idea of a 1/6 power-velocity model. Analysis of the amplitudes of first arrivals revealed large errors in the data due to variations in the geophone sensitivities and shot strengths; a least-squares method, that uses data redundancy was employed to eliminate them.
Gangi, A. F.↗
Analysis of time dependent phenomena observed with the LPSP OSO-8 instrument
Data obtained by the Laboratoire de Physique Stellaire et Planetaire's ultraviolet spectrometer onboard the OSO-8 spacecraft were analyzed in an effort to dynamically model the solar chromosphere as an aid in enhancing knowledge of the dynamical processes themselves and of spectral line formation in the dynamic chromosphere. Repeated spectral scans of strong, optically thick resonance lines formed in the solar chromosphere were examined for indications of oscillatory velocities and intensities among other indications of velocity which were studied, the blue peak is reasonably well defined, and the position of a parabolic filter fitted by the least squares method was used to define it. Observed chromospheric oscillation periods are discussed as well as the variations in altitude of the emitting region which result primarily from the motion up and down during the oscillation.
Leibacher, J. W.↗
Compositional inhomogeneities in a single Icelandic tholeiite flow
New trace element analyses of 25 basalt samples from a vertical traverse in an 11 m thick flow of Icelandic tholeiite show compositional differences which exceed analytical uncertainties and are random with respect to height. These variations suggest a short-range segregation model in which the amounts of phenocrysts, groundmass materials, and residual liquid vary randomly in different samples of the flow; a least-squares method is applied to determine if these variations reflect different proportions of crystallizing phases and residual liquid. Monte Carlo computations indicate that short-range segregation results in inhomogeneity of a magnitude of interflow compositional differences; this causes incoherence in elements with different geochemical behaviors while preserving coherence in elements of similar behavior.
Lindstrom, M. M.↗